First-order covariant differential operators

An internal description of the class of all nonlinear differential operators of the first order on the space of collections consisting of continuously differentiable vector and scalar fields on $\mathbb{R}^3$ is given. Operators of this class are invariant with respect to translations of $\mathbb{R}^3$ and are transformed by the covariant way under rotations of $\mathbb{R}^3$.